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1) I have done a lot of bad things to them, so now I have to make amends to them.

2) I have been depraved for a while, drinking, smoking ect, so now I have to make amends.

it seems to me that " to make amends" has two meanings: first to make up for/ to compensate eg in the #1

and Second to bettter oneselft and turn into a new leaf like # 2 ( try to become a good person).

What is the real meaning of " to make amends"? please give some example sentences.

Thank alot for your time and efforts.
Comments 
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'To make up for/ to compensate'. 'To better oneself' is just one way to accomplish this. There are plenty of examples available if you google the phrase.
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The usual phrase in the meaning of "to repay, or compensate for) is:
make amends for (what I did wrong) with (the party that was hurt)
I must make amends for my spreading lies with my friend.
Although "with" is more frequent, sometimes "to" is used.